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A Positivity-Preserving Finite Volume Scheme for Nonequilibrium Radiation Diffusion Equations on Distorted Meshes.

Di Yang1, Gang Peng2, Zhiming Gao2

  • 1Graduate School of China Academy of Engineering Physics, Beijing 100088, China.

Entropy (Basel, Switzerland)
|March 25, 2022
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This study introduces a new finite volume scheme for simulating nonequilibrium radiation diffusion equations. The method ensures positivity and works efficiently on distorted meshes, demonstrating strong performance in numerical tests.

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Area of Science:

  • Computational physics
  • Numerical analysis
  • Scientific computing

Background:

  • Nonequilibrium radiation diffusion equations are crucial in various physics and engineering fields.
  • Simulating these equations on distorted meshes presents significant numerical challenges, particularly in preserving solution positivity.
  • Existing methods often struggle with complex mesh geometries and maintaining solution stability.

Purpose of the Study:

  • To develop a novel positivity-preserving finite volume scheme for nonequilibrium radiation diffusion equations.
  • To enable accurate simulations on distorted meshes using fixed stencils.
  • To enhance computational efficiency in solving the resulting nonlinear systems.

Main Methods:

  • A new finite volume scheme employing fixed stencils for cell-centered and cell-vertex unknowns.
  • Utilizes a nonlinear two-point flux approximation, decoupling positivity requirements from interpolation.
  • Incorporates Anderson acceleration for efficient Picard iteration to solve nonlinear systems.

Main Results:

  • The proposed scheme demonstrates strong positivity-preserving properties on distorted meshes.
  • Numerical simulations confirm the scheme's efficiency and accuracy.
  • The method successfully handles both cell-centered and cell-vertex unknown formulations.

Conclusions:

  • The developed finite volume scheme offers a robust and efficient solution for simulating nonequilibrium radiation diffusion.
  • Its positivity-preserving nature and fixed stencil design make it suitable for complex meshing scenarios.
  • The scheme provides a valuable tool for researchers and engineers working with radiative transfer problems.